(1) Two rectangular plates of sides “a” and “b” are placed so that an upwards vertical electric field “Eo” is established between both. Calculate the electric charge in each plate.

Solution.-

In order to find the connection between the electric field Eo between the plates and the charge on a plate consider a Gaussian surface as it is shown in the sketch:

(2) In the region between two parallel plates separated by a distance d and loaded with opposite electric charges, a horizontal and uniform electric field has been established.  A little ball of mass m and positive electric charge Qo,  is placed at rest at the positive plate.  Sometime t later the ball hits the negative plate. Ignoring the effects of the Gravity, determine (a) the magnitude of the electric field (b) the velocity of the little ball when it hits the negative plate. (c) The kinetic energy of the charged particle when arriving at the negative plate.

 Solution

 Once the positively charged ball is placed close to the positive plate the former is repelled by the repulsive electrical force of the latter, hence the ball acquires acceleration. According to Newton     F = ma    and  electric field is   E = F/Q   then:

Solution

 (4) In the electric motor of an UFO that fell down in Cuzco, Peru, an electric condenser was found. The condenser consisted of two parallel plates of 20 cm x 30 cm, and between them an electric field of 50000 N/C was detected. Determine the electric charge in each plate.

Solution

The charged particle is horizontally accelerated by the horizontal electric field between the plates and vertically accelerated by the acceleration of the gravity, which is downwards. Since the particle is simply placed, its initial velocity is zero (V_ox = V_oy = 0):

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